A priori prediction of liquid-phase non-idealities and fluid-phase equilibria has played a key role in modern chemical process and product development. A number of such predictive thermodynamic models have been widely used with either qualitative or semi-quantitative accuracy. Examples include group contribution method, i.e., Universal Quasi-Chemical Functional-Group Activity Coefficients (UNIFAC), conceptual segment approach, i.e. Non-Random Two-Liquid Segment Activity Coefficients (NRTL-SAC), and solvation thermodynamics approach, i.e. Conductor Like Screening Model for Real Solvents (COSMO-RS) and Conductor Like Screening Model for Segment Activity Coefficients (COSMO-SAC).
The group contribution method is one of the earliest of the prediction models. Among the group contribution methods, UNIFAC is the most accurate and widely used. UNIFAC defines chemical compounds and their mixtures in terms of tens of predefined chemical functional groups. Binary interaction parameters which account for inter-molecular interactions between functional groups are first optimized from millions of available experimental phase equilibrium data for thousands of molecules structured with the predefined functional groups. They are then employed to predict liquid-phase non-idealities, i.e., activity coefficients, of molecules in mixtures with the predefined functional groups. UNIFAC fails for molecules with functional groups not included in the predefined UNIFAC functional group database, and it is unable to distinguish between isomers as the same set of functional groups is present. Additionally, UNIFAC yields poor predictions for molecules with complex rigid molecular structure as the functional group additivity rule is applicable only to linear molecules.
In contrast, NRTL-SAC defines four conceptual segments each uniquely representing molecular fragments exhibiting hydrophobic, polar attractive, polar repulsive, and hydrophilic nature in molecular interactions. Like UNIFAC, binary interaction parameters for the four conceptual segments are identified from available experimental data of selected reference molecules that exhibit hydrophobicity, polarity, and hydrophilicity. Conceptual segment numbers of the concerned molecules, similar to numbers and types of functional groups in UNIFAC, are the NRTL-SAC model parameters, and they are determined from experimental data of the molecule in the presence of reference solvents. Because the conceptual segment numbers are pure component parameters, NRTL-SAC can then be used to predict phase behavior of the molecule in other solvents and solvent mixtures as long as conceptual segment numbers are known for the solvents.
Solvation thermodynamics-based models have received increased attention in recent years. Among the solvation thermodynamics-based models, conductor-like screening models (COSMO) are the most widely used. There are two different variants of COSMO, i.e., COSMO-RS and COSMO-SAC. Unlike UNIFAC and NRTL-SAC, this method determines the interaction between molecules based on a so called sigma profile, i.e., a histogram of charge density distribution over the molecular surface based on molecular structure and quantum mechanical calculations. Used together with a statistical thermodynamic expression, the resultant charge density distributions are used to compute chemical potentials of molecules in solution. The solvation thermodynamic models are advantageous over UNIFAC and NRTL-SAC when no experimental data are available. However, the COSMO models require knowledge of molecular structure and conformation to generate sigma profiles from quantum mechanical calculations, and the prediction quality of the COSMO models is qualitative in nature and often considered less reliable than that of UNIFAC and NRTL-SAC. In practice, there is a need to find a way to use the COSMO models without knowledge of molecular structure. Also, empirical treatments are proposed to correct the difference between the model predictions and the experimental data.